Improving the asymmetric stochastic volatility model with ex-post volatility: the identification of the asymmetry

Abstract

Simulation studies show that the asymmetry stochastic volatility (ASV) models may infer erroneous correlation coefficients, due to their predetermined return-volatility specification. We propose identifying the correlation parameter by incorporating the ex-post volatility in the ASV framework. We obtain a significantly smaller magnitude in the estimated correlation coefficients between equity and volatility processes among major U.S. equity market indexes. Out-of-sample index return distribution forecasts demonstrate superior performance when jointly estimating the return and the ex-post volatility processes. The corrected return-volatility correlations by estimating proposed ASV models with subsample data further document the time-varying leverage effect.